Abstract
Some characterizations of fuzzy prime Boolean filters of IMTL-algebras are given. The lattice operations and the order-reversing involution on the set PB(M) of all fuzzy prime Boolean filters of IMTL-algebras are defined. It is showed that the set PB(M) endowed with these operations is a complete quasi-Boolean algebra (a distributive complete lattice with an order-reversing involution). It is derived that the algebra M/F, which is the set of all cosets of F, is isomorphic to the Boolean algebra {0, 1} if F is a fuzzy prime Boolean filter. By introducing an adjoint pair on PB(M), it is proved that the set PB(M) is also a residuated lattice.
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